Plotting Mode Shapes

Hi All. I am wondering if someone may explain to me how I should plot the mode shapes of function if the function basically has two variables say x and y. The function is described as sin(pi*x/a).*sin(pi*y/b)where a and b are constants and pi is in radians. I tried using the contour function and the program tells me the function Z has to be 2x2 or greater which leaves me blank. I have written the code below if one wants to take a look. I appreciate any assistance:

clear all
clc
format short e
syms

%%Data:
EL = 38.6e9;
GLT = 4.14e9;
ET = 8.27e9;
vLT = 0.26;
rho = 1.8;
a = 1;
b = 0.5;
H = 0.005;
n = 2;
h = H/n;
h0 = 0;
h1 = h0+h;
h2 = h1+h;
x = linspace(-10,10,1);
y = linspace(-10,10,1);

%%Calculate vTL and rho_0:
vTL = (vLT*ET)/EL;
rho_0 = rho*h*(h1-h0) + rho^2*h*(h2-h1);

%%1st Layer:
%%Calculate Transformation Matrix:
Theta = 90;
Theta = (Theta*pi)/180;
m = cos(Theta);
n = sin(Theta);
T1 = [m^2 n^2 2*m*n;n^2 m^2 -2*m*n;-m*n m*n m^2-n^2];
T2 = [m^2 n^2 m*n;n^2 m^2 -m*n;-2*m*n 2*m*n m^2-n^2];

%%Calculate Q Matrix:
Q11 = EL/(1-vLT*vTL);
Q12 = (ET*vLT)/(1-vLT*vTL);
Q22 = ET/(1-vLT*vTL);
Q66 = GLT;
Q = [Q11 Q12 0;Q12 Q22 0;0 0 Q66];

%%Calculate Q_bar Matrix:
Q_Bar_90 = inv(T1)*Q*T2;

%%2nd Layer:
%%Calculate Transformation Matrix:
Theta = 0;
Theta = (Theta*pi)/180;
m = cos(Theta);
n = sin(Theta);
T1 = [m^2 n^2 2*m*n;n^2 m^2 -2*m*n;-m*n m*n m^2-n^2];
T2 = [m^2 n^2 m*n;n^2 m^2 -m*n;-2*m*n 2*m*n m^2-n^2];

%%Calculate Q Matrix:
Q11 = EL/(1-vLT*vTL);
Q12 = (ET*vLT)/(1-vLT*vTL);
Q22 = ET/(1-vLT*vTL);
Q66 = GLT;
Q = [Q11 Q12 0;Q12 Q22 0;0 0 Q66]

%%Calculate Q_bar Matrix:
Q_Bar_0 = inv(T1)*Q*T2;

%%Calculate the D Matrix:
D11 = (1/3)*Q_Bar_90(1,1)*(h1^3-h0^3)+(1/3)*Q_Bar_0(1,1)*(h2^3-h1^3);
D12 = (1/3)*Q_Bar_90(1,2)*(h1^3-h0^3)+(1/3)*Q_Bar_0(1,2)*(h2^3-h1^3);
D16 = (1/3)*Q_Bar_90(1,3)*(h1^3-h0^3)+(1/3)*Q_Bar_0(1,3)*(h2^3-h1^3);
D21 = (1/3)*Q_Bar_90(2,1)*(h1^3-h0^3)+(1/3)*Q_Bar_0(2,1)*(h2^3-h1^3);
D22 = (1/3)*Q_Bar_90(2,2)*(h1^3-h0^3)+(1/3)*Q_Bar_0(2,2)*(h2^3-h1^3);
D26 = (1/3)*Q_Bar_90(2,3)*(h1^3-h0^3)+(1/3)*Q_Bar_0(2,3)*(h2^3-h1^3);
D16 = (1/3)*Q_Bar_90(3,1)*(h1^3-h0^3)+(1/3)*Q_Bar_0(3,1)*(h2^3-h1^3);
D26 = (1/3)*Q_Bar_90(3,2)*(h1^3-h0^3)+(1/3)*Q_Bar_0(3,2)*(h2^3-h1^3);
D66 = (1/3)*Q_Bar_90(3,3)*(h1^3-h0^3)+(1/3)*Q_Bar_0(3,3)*(h2^3-h1^3);
D = 2*[D11 D12 D16;D12 D22 D26;D16 D26 D66]

%%First Frequency:
m = 1;
n = 1;
w11 = sqrt((pi^4/rho_0)*(D11*(m/a)^4+2*(D12+2*D66)*(m/a)^2*(n/b)^2+D22*(n/b)^4))
Mode11 = sin(pi*x/a).*sin(pi*y/b);
contour(x,y,Mode11)
%%Second Frequency:
m = 1;
n = 2;
w12 = sqrt((pi^4/rho_0)*(D11*(m/a)^4+2*(D12+2*D66)*(m/a)^2*(n/b)^2+D22*(n/b)^4))
Mode12 = Mode11 + sin(pi*x/a).*sin(pi*y/b);
%%Third Frequency:
m = 1;
n = 3;
w13 = sqrt((pi^4/rho_0)*(D11*(m/a)^4+2*(D12+2*D66)*(m/a)^2*(n/b)^2+D22*(n/b)^4))
Mode13 = Mode11 + Mode12 + sin(pi*x/a).*sin(pi*y/b);

And here is what I get after running the code:

??? Error using ==> contour at 73
Z must be size 2x2 or greater.

Error in ==> qn_b at 82
contour(x,y,Mode11)

Thank you.

Answer 1

[Muhammad Sardar Khan]

refer to this line: Mode11 = sin(pi*x/a).*sin(pi*y/b); since x and y are vectors created by the linspace function above. The multiplication will require a dot, because multiplication of pi with each element is required. As this expression will enter into the contour plot as a variable Z, and mandatory requirement for Z is such that it has size of 2x2 or more, best luck!

[Manish Chauhan]

put this

%x=linspace(0,a,100);

% y=linspace(0,b,100);

% [xx,yy]=meshgrid(x,y);

and change Mode11 = sin(m*pi*x/a).*sin(*pi*y/b);

put x to xx and y to yy